Chapter 6. Lateral diffusion in membranes

P.F.F. Almeida and W.L.C. Vaz
Universidade do Algarve, Unidade de Ciëncias Exactas e Humanas,
P-8000 FARO, Portugal
Present address of P.F.F. Almeida: University of Virginia, Department of Pharmacology,
Charlottesville, VA 22908, USA

1. Introduction

The basis of the cell membrane is a bilayer of lipid molecules where proteins are either embedded (integral proteins) or surface-adsorbed (peripheral proteins) [135]. These lipids are elongated, amphiphilic molecules, which, in aqueous media, spontaneously self-organize so that their hydrophilic headgroups are exposed to water and their hydrophobic 'tails' are hidden from it. Among the possible structures that result from these requirements is the two-dimensional bilayer membrane, which extends in a plane perpendicular to the long axis of the lipid molecules. Thermal agitation induces the movement of lipids and integral proteins in the plane of the lipid bilayer. This thermal movement in two dimensions is identical with lateral diffusion [35]. Although a complete treatment must include both rotational and translational diffusion, for biological membranes translational diffusion is by far the most important, and we shall restrict our attention to this aspect.

The theoretical and experimental aspects of lateral diffusion of lipids and proteins in lipid bilayer membranes have been reviewed by Clegg and Vaz [24] up to 1984. The present article is conceived as a sequel of that work. Repetition of discussions will be generally avoided. For instance, the conceptual questions arising in each theory of diffusion in lipid bilayers will be treated in a much more concise manner. The reader is referred to [24] for more details. We shall focus instead on the development in the field from 1984 to 1993.

Two theories of diffusion in homogeneous bilayers were given more emphasis by Clegg and Vaz [24]. The first is a continuum hydrodynamic model for diffusion of particles the size of which is much larger than that of the solvent. This model is thus best applicable to diffusion of integral membrane proteins in lipid bilayers. The second is a free-volume model, which takes into account the discreteness of the lipid bilayer and is thus best suited to describe lipid diffusion. These two models have been used most often and with best results in the interpretation of experimental data. They will be briefly discussed, emphasizing recent work.

A problem not discussed by Clegg and Vaz, except in connection with Stoke's paradox [71, 117, 174], is that of the definition of a diffusion coefficient in two dimensions. This problem will be reviewed here, not because there was progress in the matter, but because some confusion has been created about it. Namely, it has become common to speak of microscopic and macroscopic diffusion coefficients, which only apparently have an experimental basis.

It appears to us that the most interesting turn that the field has taken, both theoretically and experimentally, has been the study of diffusion in heterogeneous membranes. These can be lipidÐprotein membranes with a high protein concentration or multi-component lipid bilayers where two or more laterally separated phases coexist.

When two phases are present in a bilayer, a new, fundamental variable parameter appears, which is the lateral connectivity of each phase. When a phase is self-connected throughout the plane of the bilayer it is said to be percolating. Conversely,
if a phase is constituted of disconnected domains it is not percolating. The percolation threshold of a given phase is the area fraction of that phase above which a percolating cluster exists. Below the percolation threshold long range diffusion in that phase cannot occur over distances larger than the dimensions of the phase domains. Phase percolation has been studied in several artificial bilayer systems [168, 169].

In a two-phase system consisting of a percolating fluid phase and a minor, impermeable phase, tracer diffusion is restricted. The problem, named 'Diffusion in an Archipelago' by Saxton [121], is to understand how the presence of obstacles (the impermeable phase) modifies tracer diffusion relative to the all-fluid state of the bilayer. Three cases falling into this general situation have been studied (experimentally or theoretically) in membranes: lipid diffusion in solid-fluid lipid systems [6], lipid diffusion in proteinÐfluid-lipid systems [14], and protein diffusion in concentrated solutions of proteins in lipid bilayers [129]. In the first case the obstacles are solid phase domains; in the second, the obstacles are integral membrane proteins; in both, the tracer is a lipid. In the third case, the tracer and the obstacles are proteins.

A related problem is diffusion in a two-phase system where both phases are fluid. In this case, which has also been studied [7], the tracer molecule can diffuse through-out the entire plane of the membrane no matter which phase percolates. The diffusion coefficient will, however, depend on the area fractions of each phase present and also on which phase is percolating.

This article will focus on some selected aspects, which we feel involve important general concepts or questions in the field of lateral diffusion in membranes. It is not intended as an extensive review of all the work on diffusion since 1984. Most
attention is devoted to diffusion in heterogeneous membranes and related problems, a choice obviously biased by our own view of the field.

First, we consider the theoretical aspects that are pertinent to diffusion in lipid bilayer membranes. A large part of this section is based on the review presented in ref. [8]. Second, we examine experimental studies in model systems and compare them with theory. Finally, we consider some studies in biological systems and the consequences that result for the function of biological membranes in general from the structural and dynamical problems associated with diffusion.

As far as experimental methods are concerned, two of them receive most attention in this article. One method is fluorescence recovery after photobleaching (FRAP) [11, 64], which has proved its usefulness during the last almost 20 years. The other
is single particle tracking (SPT) [46, 48, 131], which although only developed in the last five years has received much attention and appears very promising. Methods such as FRAP, nuclear magnetic resonance (NMR) [70, 82, 173], or dissipation of electron spin resonance (ESR) signal gradients [31, 134] measure diffusion over large distances, whereas methods based on bimolecular reactions, such as Heisenberg spin exchange [97, 115, 153] or fluorescence quenching [43], and neutron scattering [107, 145] measure diffusion over short distances. Single particle tracking can in principle measure diffusion over small and large distances, depending on the time of observation and spatial resolution of the measuring device, but it is normally restricted to relatively small distances.

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